# Steady State Response of a RL Circuit with Sinusoidal Input

The figure below shows the RL circuit from problem 10.9-6 of Introduction to Electric Circuits, 5e by R.C. Dorf and J.A. Svoboda. The input to this circuit is the current

provided by the current source. (M is the magnitude of the input, in Amps, and is phase angle of the input, in degrees.) The response, or output, of the circuit is the current i2(t). The network function

describes the relationship between the phasors corresponding to the input, i1(t), and the output, i2(t). In this case so

The steady state response of this circuit is given by

The values of the parameters M and of the input sinusoid, as well as the values of the resistance R and inductance L, can be changed using the scrollbars.

Suggestions:

1. Set M=2 A, =-15 deg, R=8 Ohms and L = 2 H to see the circuit in Problem 10.6-9.

2. Set M=5 A, R=8 Ohms and L = 2 H. Vary .

3. Set M=5 A, =45 deg and L = 5 H. Vary R.

4. Set M=5 A, =45 deg and R=10 Ohms. Vary L.

5. Set M=5 A. Vary R and L until i2(t) is half as large as i1(t). Reconsider the equations given above for i1(t) and i2(t) in light of the values that you found for R and L.

6. Set M=5 A. Vary R and L until the phase difference between i2(t) and i1(t) is 45 degrees. Reconsider the equations given above for i1(t) and i2(t) in light of the values that you found for R and L.